Recently, Nano-encapsulated phase change materials (NEPCM) have attracted the attention of researchers due to their promising application in thermal management. This research investigates magnetohydrodynamic mixed convection of NEPCM contained within a lid-driven trapezoidal prism enclosure containing a hot-centered elliptical obstacle. The upper cavity wall is moving at a constant velocity; both inclined walls are cold, while the rest of the walls are insulated. The Galerkin Finite Element Method was used to solve the system's governing equations. The influence of Reynolds number (Re 1-500), Hartmann number (Ha = 0-100), NEPCM volumetric fraction φ (0-8%), and elliptical obstacle orientation α (0-3π/4) on thermal fields and flow patterns are introduced and analyzed. The results indicated that the maximum heat transfer rate is observed when the hot elliptic obstacle is oriented at 90°; an increment of 6% in the Nu number is obtained in this orientation compared to other orientations. Reducing Ha from 100 to 0 increased Nu by 14%. The Maximum value of the Bejan number was observed for the case of Ha = 0, α = 90° and φ = 0.08.
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